A pure breed chicken is made when you have two chickens of the same breed that make that chick. For example: if you had a rhode island red rooster fertilize eggs from a rhode island red hen, and you incubated those eggs then you would get a pure rhode island red chick.
Purebred doesn't mean much because hatchery birds can be purebred but look nothing like the standards. What really counts is standard bred chickens, birds that are bred and selected to be as close to the standard of perfection. I have many purebred chickens in my laying flock, but my standard bred brahmas are on another level.